CN111079075B - Non-2-base DFT optimized signal processing method - Google Patents

Abstract

The invention belongs to the field of digital signal processing, optimizes a Cooley-Tukey algorithm based on non-2-base DFT, and discloses a signal processing method optimized by non-2-base DFT, which optimizes the prime factor decomposition of the Cooley-Tukey algorithm, disassembles N-point DFT according to the prime factor decomposition, and processes signals by using the Cooley-Tukey algorithm on the basis. The invention improves the reliability of signal processing and the accuracy of fixed-point calculation processing, and reduces the difficulty of signal processing of fixed-point non-2-base N-point DFT.

Description

A Signal Processing Method Based on Non-2-radix DFT Optimization

technical field

The invention belongs to the field of digital signal processing, and relates to a non-2-radix DFT optimized signal processing method in a 5G system, mainly aiming at engineering realization optimization of a non-2-base N-point DFT prime factorization algorithm in digital signal processing. It is convenient for fixed-point processing of DSP, reduces the difficulty of developing non-2-base N-point DFT, and has certain universality and universality.

Background technique

In the 5G mobile communication system, in order to meet the physical layer design performance of the system, fixed-point DFT is widely used in the process of digital signal processing. For example, when processing Sounding signals, the signal length is 273, and non-2-base DFT is required for processing. The 2-base DFT can be realized directly by a very mature FFT algorithm. For non-2-radix N-point DFT, there are roughly two ways to implement it: one is to interpolate N points to obtain base-2 M points, use base-2 or base-4 to realize the FFT of M points, and then reduce Sampling to obtain non-2-base N-point DFT; the second is to decompose N into prime factorization, and iteratively calculate the DFT of each prime factor point to obtain the DFT of N points, among which Prime-factor FFT algorithm (PFA) and The Cooley-Tukey algorithm is the two most commonly used algorithms at present. Coprime factor algorithm, also known as Good-Thomas algorithm, its principle is to convert N-point DFT into a two-dimensional DFT of N1×N2 size, and then continue to recursively use PFA on N1 (or N2) until it cannot be decomposed. The disadvantage of the PFA algorithm is that N1 and N2 are required to be mutually prime, so when decomposing the prime factor of N, if there is a power of the prime factor in the decomposition result, the PFA algorithm cannot be applied. The Cooley-Tukey algorithm is derived from the mixed-radix algorithm. The same as the PFA algorithm, the Cooley-Tukey algorithm also converts the N-point DFT into a two-dimensional DFT of N1×N2 size, and then iterates it. Although the calculation steps Compared with the PFA algorithm, there are more processes of multiplying the Twiddle factors (Twiddle factors), but different from the PFA algorithm, the N1 and N2 of the Cooley-Tukey algorithm do not need to be prime, which makes the algorithm have good universality. When using the Cooley-Tukey algorithm to implement DFT calculations, especially in fixed-point DFT calculations, the development of the entire process from decomposing prime factors to DFT calibration compensation is relatively complicated, and the calibration accuracy cannot be guaranteed.

Contents of the invention

The purpose of the present invention is to provide a non-2-radix DFT optimized signal processing method, improve the reliability of signal processing and the accuracy of fixed-point calculation processing, and reduce the signal processing difficulty of fixed-point non-2-radix N-point DFT.

The non-2-base DFT optimized signal processing method provided by the present invention is based on the Cooley-Tukey algorithm, optimizes the prime factor decomposition of the Cooley-Tukey algorithm, disassembles the N-point DFT according to the prime factor decomposition, and uses the Cooley-Tukey algorithm on this basis. The Tukey algorithm processes the signal; the prime factorization is specifically: for a fixed-point non-2-basic signal of length N, perform prime factorization on N, N=N ₁ ×N ₂ ×…×N _i , where N _m is Prime number, and repeatable, m ∈ {1, 2, ..., i}; dismantling the N-point DFT is specifically: arrange all N _m in descending order, and the arranged order is {N′ ₁ , N′ ₂ ,...,N′ _i }, set the factor set according to N′ ₂ N′ ₃ …N′ _i ×N′ ₁ , N′ ₃ N′ ₄ …N′ _i ×N′ ₂ , N′ ₄ N′ ₅ … N' _i ×N' ₃ ,..., N' _i ×N' _i-1 is divided into i-1 matrices.

The Cooley-Tukey algorithm needs to calculate the DFT factor and the Twiddle factor when processing the signal. After the prime factor decomposition is optimized, the calculation of the DFT factor and the Twiddle factor is adjusted. Specifically, the calculation of the DFT factor is based on dismantling the N-point DFT , generate DFT factors according to the arranged factor set {N′ ₁ , N′ ₂ ,…, N′ _i }, and calibrate the DFT factors; calculate Twiddle factors: on the basis of dismantling the N-point DFT, according to the division The matrix of generates Twiddle factors and scales the Twiddle factors.

The present invention also includes calculation of calibration compensation, calibration supplement is used to measure and calculate the actual signal power usage, on the basis of dismantling N-point DFT, the factor set {N′ ₁ , N′ ₂ ,…, N′ _i } is calibrated Compensation calculation for the scale back value: B=([log ₂ N′ ₁ ]+[log ₂ N′ ₂ ]+…+[log ₂ N′ _i ])×r, where B is the number of calibration compensation bits, and r is Scale integer bit count.

The processing of the signal in the present invention is specifically: (1) for the N _m point DFT of m<i, the signal is divided into N' _m+1 N' _m+2 ...×N' _i groups, and each group is respectively connected with the mth group DFT The multiplication and addition of factors is calculated as the output of N _m -point DFT; N′ _m+1 N′ _m+2 …×N′ _i group of N _m -point DFT outputs are multiplied by the mth group of Twiddle factors respectively, and the obtained results are obtained as N' _m+1 N' _m+2 ...×N' _i -point DFT input, wherein, when m=1, the signal refers to the fixed-point non-2-base signal of the original input, and in other cases the signal refers to N The output of _{the m-1} point DFT is multiplied by the m-1th group of Twiddle factors; (2) execute (1) step i-1 times; (3) calculate the N' _i point DFT: use N' _i-1 The result of multiplying the point DFT with the corresponding Twiddle factor is to calculate the N′ _i point DFT by iterating N′ _i-1 , N′ _i-2 , ... N′ ₂ times from the inner layer to the outer layer respectively; (4) for N′ _i The output of the point DFT is output after rearranging the order.

The present invention has the following beneficial effects: on the basis of the original Cooley-Tukey algorithm, the present invention optimizes and improves processes such as decomposing prime factors, dismantling N-point DFT, calculating DFT factors, calculating Twiddle factors, and calculating calibration compensation. Through the optimization of the algorithm, the process of decomposing the prime factor, dismantling the N-point DFT, calculating the DFT factor, calculating the Twiddle factor, and calculating the calibration compensation is realized, which makes the original tedious and complicated calculation process simple and reduces the non-2 -The difficulty of the signal processing of base DFT; Simultaneously the present invention can revise calibration according to different needs, calculates and feeds back calibration compensation result, has guaranteed the precision of signal processing; And after being optimized, is convenient to the modularization of Cooley-Tukey algorithm iterative operation Realization, the reliability of signal processing is improved, and the present invention is applicable to any non-2-base DFT or IDFT.

Description of drawings

Figure 1 is a schematic diagram of the calculation process of decomposed prime factor, DFT factor, Twiddle factor, and calibration compensation;

Figure 2 is a schematic diagram of the first step of splitting the 273-point DFT algorithm;

Figure 3 is a schematic diagram of the second step splitting of the 273-point DFT algorithm;

Fig. 4 is a schematic diagram of 273-point DFT algorithm data processing mapping relationship;

Fig. 5 is a flowchart of the present invention.

Detailed ways

In order to make the purpose, technical solution and advantages of the present invention more clear and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and technical solutions.

The invention is a further improvement on the basis of the Cooley Tukey algorithm, which is beneficial to modular realization. As shown in Figure 5, it includes decomposing prime factors and scaling, performing DFT split calculation and sequence rearrangement.

As shown in Figure 1, in the process of decomposing the prime factor and scaling, decompose the prime factor of the non-2-base time domain sequence to be calculated by DFT, disassemble the N-point DFT, calculate the DFT factor, calculate the Twiddle factor, and calculate the constant standard compensation. These optimized processing procedures can be realized by software. These processing flows only need to take the non-2-base time-domain sequence length N as input, and output DFT factors, Twiddle factors, prime factors (including repeated factors), and scaling compensation. Among them, there is no order requirement for calculating the DFT factor and calculating the Twiddle factor. The DFT factor and the Twiddle factor are used in the calculation of the present invention, the prime factor determines the split structure of the non-2-base time domain sequence, and the calibration compensation is used in the calculation of the actual signal power.

Decompose the prime factor: Decompose the prime factor of the length N of the DFT sequence, and record all the factors for dismantling the N-point DFT process. The number of factors is recorded as i, and the number of factors determines the number of iterative calculations required for the N-point DFT; N=N ₁ ×N ₂ ×...×N _i , where N _m are all prime numbers and can be repeated, m∈{1,2,...,i}.

Disassemble N-point DFT: Based on the decomposition of prime factors, arrange all factors N _m from large to small, and the arranged order is {N′ ₁ , N′ ₂ ,…, N′ _i }, Set the factor set according to N′ ₂ N′ ₃ …N′ _i ×N′ ₁ , N′ ₃ N′ ₄ …N′ _i ×N′ ₂ , N′ ₄ N′ ₅ …N′ _i ×N′ ₃ ,… , N′ _i ×N′ _i-1 is divided into i-1 matrices for the calculation of Twiddle factors, DFT calculation and multiplication with Twiddle factors.

Calculation of DFT factors: Based on the dismantling of N-point DFT, DFT factors are generated according to the set of arranged factors, and the DFT factors are calibrated. For i factors, when calculating DFT factors, loop i times.

Calculation of Twiddle factors: Based on the dismantling of N-point DFT, Twiddle factors are generated according to the divided matrix, and the Twiddle factors are calibrated. For i factors, when calculating Twiddle factors, loop i-1 times.

Calculation of calibration compensation: based on the dismantling of N-point DFT, the factor set {N′ ₁ , N′ ₂ ,…, N′ _i } obtained after dismantling and permutation is calculated for calibration fallback value compensation:

Wherein B is the number of calibration compensation bits, and r is the number of integer calibration bits. For the DFT calibration value Q(a, b), r=a-b, wherein a is the calibration bit number of the floating point number, and b is the calibration number of the calibration number. decimal places. The calibration compensation B of the N-point DFT can be obtained through the calculation of this formula.

Combined with Figures 2, 3, 4, and 5, taking the DFT with a full bandwidth of 273 PRB in the 5G system as an example, the implementation of DFT split calculation and sequence rearrangement will be described in detail. After decomposing the prime factor of 273, we get 13×7×3 (it has been sorted from large to small, set N ₁ =13, N ₂ =7, N ₃ =3), so the 273-point DFT is divided into three steps to complete: The first step is to calculate the 13-point DFT and multiply it with the first set of Twiddle factors; the second step is to calculate the 7-point DFT and multiply it with the second set of Twiddle factors; the third step is to calculate the 3-point DFT; the fourth step is to rearrange the output results .

The first step is shown in Figure 2. The first step is composed of 21 13-point DFTs. The input time domain sequences are grouped according to modulo 21 and divided into 21 groups, which are used as the input of 13-point DFT. In each group of 13-point DFT, the The input signal of this group is multiplied and added to the first group of DFT factors (m=1), and the calculation result is used as the output of the group of 13-point DFT. The output of each group of 13-point DFT is multiplied by the first group of 21×13 Twiddle factors (m=1) as the input of the next 21-point DFT, and it needs to satisfy the output of the kth group in the first step as the second step for each group The conditions of the kth input are sorted. For example, in Figure 2, the output of the first group of 13-point DFT (the top in Figure 2 is the first group) is multiplied by the first group of 21×13 Twiddle factors as each group The first input of 21-point DFT, the output of the second group of 13-point DFT is multiplied by the first group of 21×13 Twiddle factors as the second input of each group of 21-point DFT, and so on, the 21st group of 13-point DFT The output of is multiplied by the first group of 21×13 Twiddle factors as the input of each group of 21-point DFT. The first step of dismantling is to establish the overall structure of the 273-point DFT, forming a 13×21 dismantling structure, that is, converting the 273-point DFT calculation into 13 recursive operations of the 21-point DFT.

The second step is shown in Figure 3. Similar to the first step, the second step is to disassemble the 21-point DFT of each iteration unit (a total of 13 groups of 21-point DFT), and disassemble it into a 7×3 structure. The output signals of the first step are grouped according to modulus 3 and divided into 3 groups. The inputs y(0) to y(20) in Figure 3 are the inputs of each group of 21-point DFT mentioned in the first step in Figure 2, y(0) to y(20) are divided into three groups as the input of each group of 7-point DFT. The output of each group of 7-point DFT is multiplied by the second group of 3×7 Twiddle factors (m=2) as the input of the third step 3-point DFT, and the output of the first group g needs to be satisfied as the second step. The conditions of the gth input of the group are sorted, for example, in Figure 3, the output of the first group of 7-point DFT (the top in Figure 3 is the first group) is multiplied by the second group of 21×13 Twiddle factors as each group The first input of the 3-point DFT, the output of the second group of 7-point DFT is multiplied by the second group of 21×13 Twiddle factors as the second input of each group of 7-point DFT, the output of the third group of 7-point DFT and the output of the first group of 7-point DFT Two groups of 21×13 Twiddle factors are multiplied as the input of each group of 7-point DFT. The second step process converts the blackjack DFT calculation into seven recursive operations of the 3-point DFT.

In the third step, the output result of the second step is calculated according to 13 times of the outer layer and 7 iterations of the inner layer to calculate the 3-point DFT to obtain the result of the entire 273-point DFT.

The order of the fourth step is rearranged. The result of the calculation in the third step cannot be used as the final output. Due to the two DFT splits, the order of the output of the third step is disrupted compared with the input of the first step. Need Combining the two splits, perform two rearrangements to achieve order adjustment, and adjust the order of the output sequence after i iterations according to the set of factors arranged during the prime factorization. From Figure 2, we can see that the output order of the 21-point DFT is disordered Yes, there is no sequential order from X(0) to X(272). From Figure 3, it can be seen that the output order of the 3-point DFT is also disordered, and there is no sequential order from Y(0) to Y(20). As shown in Figure 4, the output after adjustment is sorted from X(0) to X(272), which corresponds to the input order of x(0) to x(272), and can be used as the final output of the 273-point DFT.

It can be seen from the examples that the optimization of the Cooley-Tukey algorithm makes the entire process clear and clear. From the aspect of engineering implementation, due to the decomposition of prime factors, dismantling of N-point DFT, calculation of DFT factors, calculation of Twiddle factors, calculation of calibration compensation, etc. The process realizes automatic processing, which greatly simplifies the difficulty of algorithm implementation; at the same time, because the computer realizes the automation of part of the algorithm process, the stability and reliability of the overall algorithm implementation are improved; the invention is universal, and can be used for any non-2 - Either base DFT or IDFT can be applied.

The above content is a further detailed description of the present invention in conjunction with specific examples. It cannot be determined that the specific implementation of the present invention is limited thereto. For those of ordinary skill in the technical field of the present invention, without departing from the inventive concept, Several simple inferences or substitutions can also be made, all of which should be considered as belonging to the scope of patent protection determined by the submitted claims of the present invention. The above description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the application. Therefore, the present application will not be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (4)

1. A non-2-base DFT optimized signal processing method is based on Cooley-Tukey algorithm, and is characterized in that: optimizing the prime factor decomposition of the Cooley-Tukey algorithm, disassembling the N-point DFT according to the prime factor decomposition, and processing the signal by using the Cooley-Tukey algorithm on the basis; the quality factor decomposition specifically comprises the following steps: for fixed-point non-2-basis signals of length N, N is prime factorized with N = N ₁ ×N ₂ ×…×N _i In which N is _m Are prime numbers and can be repeated, and m belongs to {1,2, \ 8230;, i }; the N-point DFT disassembly specifically comprises the following steps: all N are _m In descending order, the sequence is { N' ₁ ，N′ ₂ ，…，N _i '} combining the factors by N' ₂ N′ ₃ …N _i ′×N ₁ ′，N′ ₃ N′ ₄ …N _i ′×N′ ₂ ，N′ ₄ N′ ₅ …N _i ′×N′ ₃ ，…，N _i ′×N′ _i-1 Divided into i-1 matrices.

2. The non-2-based DFT optimized signal processing method as recited in claim 1, wherein: calculating a DFT factor: based on the N-point DFT, according to the arranged factor set { N } ₁ ′，N′ ₂ ，…，N _i ' } generating DFT factors and scaling the DFT factors; computing Twiddle factor: and on the basis of disassembling the N-point DFT, generating a Twdle factor according to the divided matrix, and calibrating the Twdle factor.

3. The non-2-based DFT optimized signal processing method as recited in claim 2, wherein: further comprising calculating a scaling compensation, combining the factors to { N' ₁ ，N′ ₂ ，…，N _i ' } carrying out calibration backspacing value compensation calculation:

where B is the number of scaled compensation bits and r is the number of scaled integer bits.

4. The non-2-based DFT optimized signal processing method as recited in claim 1,2 or 3, further comprising: the signal processing specifically comprises: (1) For N of m < i _m Point DFT, divide the signal into N' _m+1 N′ _m+2 …×N _i ' groups, each group being respectively multiplied and added with the m-th group DFT factors as N _m Outputting a point DFT; n' _m+1 N′ _m+2 …×N _i ' group N _m The outputs of the point DFTs are multiplied by the m-th group Twdle factors, and the result is N' _m+1 N′ _m+2 …×N _i ' Point DFT input, wherein when m =1, the signal refers to the fixed-point non-2-base signal of the original input, and the rest of the signal refers to N _m-1 The result of multiplying the output of the point DFT by the (m-1) th set of Twdle factors; (2) performing step i-1 of step (1); (3) Calculating N _i ' Point DFT: is N' _i-1 The result of multiplying the point DFT by the corresponding Twdle factor is iterated by N 'from inner layer to outer layer respectively' _i-1 ，N′ _i-2 ，…N′ ₂ Sub-calculation of N _i ' Point DFT; (4) To N _i The output of the' point DFT is output after being rearranged in order.

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